It is very unlikely that the problem is lack of O2. The problem with the air in big cities is CO and hydrocarbons from cars and the products made from this by sunlight, alltogether called "smog". Moscow is famous for underground peat fires in the vicinity :=(
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GeorgJun 3 '11 at 13:57

Hence the idea - if you can mainain oxygen/CO2 level in isolated environment, you can easily filter out all the dirt & contaminants. Continiously filtering all incoming air from ventilation is going to be very expensive.
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BarsMonsterJun 3 '11 at 15:25

""Continiously filtering all incoming air from ventilation is going to be very expensive. "" How do You know? Without any knowledge of methods and the cost?
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GeorgJun 3 '11 at 16:15

3 Answers
3

Here is a Babelfish translation from German Wiki on Life support systems. (Including NASA!)
(English WIKI on the topic is very bad)

*

In order to make for humans possible a
surviving, the supply of breathable
gas (thus air) must be guaranteed. But
air must be as free of harmful
substances as possible and determined
parameters keep. Thus on board EAT a
total pressure from 97,9 to 102.7 kPa,
an oxygen partial pressure from 19,5
to 23.1 kPa, a nitrogen partial
pressure of less as 80 kPa and a
carbon dioxide partial pressure of
less as 1 kPa than acceptable
regarded. The air temperature in EAT
is appropriate (adjustable) between
18,3 and 26,7 °C. By the air condition
technology an air humidity between 25
and 75% and a constant air movement
between 0,05 and 1,0 m/s are secured,
in order to avoid microbe growth and
fungus growth on the one hand and a
too dry air (danger of the sparking)
on the other hand. Here usually
conventional air conditioning systems
with refrigerants (e.g. ammonia or
Freon) are used. Around air thereby
condensing heat exchangers will
dehumidify begun. [2] For carbon
dioxide connection re-usable zeolites
or solid amines, in space suits are
used also lithium hydroxide. The
production of oxygen takes place
usually via the electrolysis from
water and partly via recuperation from
the carbon dioxide by Sabatier process
and the following methane pyrolysis.
As Backup or with short term
employment oxygen also compressed or
chemical reactions is used to the
supply of oxygen. Pollutants are
constantly supervised by appropriate
measuring methods like for example
mass spectrometers and gas
chromatography and by molecular sieve,
activated charcoal or lithium
hydroxide filtered. In submarines
similar values are valid, and partly
also similar processes are used. [3]

Think: NASA did/does very different depending on situation! On a spacestation with ample electricity You can do electrolysis, for Apollo they made electricity from oxygen/hydrogen in fuel cells! And cost of upmass includes the cost of energy generators or storage batteries.

But topic here is some (realistic) method for barsmonster to survive the Moscow summer. This is best done by cooling the air intake, demoist it (which would hopefully remove some of the organic "smog" particles) and one could try some PP microfibre filters. The exhaust air would be used to cool down the air taken in. Any separation of carbon dioxide by ad(ab)sorbents would be much more expensive than this air exchange.

There is no inorganic method of which I am aware that is not "messy." They all consume and/or produced something extraneous to the clean reaction you want ---> CO2 + energy = C + O2.

NASA (these are the people who should know) use electrolysis on the ISS to split 2 H2O into 2 H2 + O2. The H2 is vented overboard, the O2 is vented to the cabin. CO2 is captured by a separate system and also vented overboard. With the cost of upmass being on the order of $10K/lb., you can bet that if there was an easy way to rip the O2 out of CO2, that they'd be doing it.

Using photosynthesis sounds like the easiest way to re-use O2 that is bound in CO2. The NET equation is 6 CO2 + 6 H2O + energy (light) ---> C6H12O6 + 6 O2. This uses half the water per liter of O2 produced as electrolysis. If the sugar produced can be consumed, then that upmass is saved also (reduces the weight of food that needs to be shipped to orbit).

Rather than just splitting water, you want to react it with the CO2 to make O2 and carbohydrates. I think this can be done with an inorganic catalyst (I'd have to Google for the details) but of course the easiest solution is to use photosynthesis.